Compressed sensing (CS) is a field of signal processing in which a sparse signal is recovered from far fewer samples than what is deemed necessary by the Nyquist sampling theorem. With CS, a signal is sampled in a pseudorandom manner. The number of samples taken is on the order of 1/10th of that needed to satisfy the Nyquist criterion. After all samples have been gathered, an L1 norm minimization technique is applied to the corresponding undetermined system of linear equations and a full resolution signal is reconstructed. With regards to hyperspectral imaging, CS approaches have been shown to provide cost savings over conventional methods. For example, a two-dimensional IR sensor costs more than a one-dimensional IR photodiode.
Processing speed and capture time are the biggest disadvantages to CS systems. The former is a result of having to solve a system of linear equations for each reconstructed signal. A conventional approach requires no processing since it directly samples the high-resolution signal. CS processing speed is being addressed with algorithm optimization and tailored hardware, e.g. FPGA/ASIC accelerators. Digital light processing (DLP®) can directly impact capture time since most CS applications employ digital micromirror devices (DMDs) to perform the pseudo-random measurements. DLP is a registered trademark of Texas Instruments Incorporated of Dallas, Tex. In these DLP applications, capture time is directly proportional to the load time of the DMD. For example, a pseudorandom binary pattern must be loaded and then the hyperspectral sensor must capture the reflected result. This is repeated until all desired patterns have been displayed.